TL;DR
This paper generalizes the F4 algorithm, originally for polynomial rings over fields, to Euclidean rings, enabling more efficient computation of Groebner bases by reducing multiple polynomials simultaneously.
Contribution
It introduces a generalized F4 algorithm applicable to polynomial rings over Euclidean rings, extending its utility beyond fields.
Findings
Enables Groebner basis computation over Euclidean rings.
Improves efficiency by simultaneous reduction of multiple polynomials.
Generalizes existing F4 algorithm to broader algebraic structures.
Abstract
This short note is the generalization of Faugere F4-algorithm for polynomial rings with coefficients in Euclidean rings. This algorithm computes successively a Groebner basis replacing the reduction of one single s-polynomial in Buchberger's algorithm by the simultaneous reduction of several polynomials.
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